Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_0^1 \frac{ e ^2(x-1)}{(x+1)^3} d x=$
A
$\frac{ e }{4}$
✓
$\frac{ e }{4}-1$
C
$\frac{e}{4}+1$
D
$\frac{ e }{2}-1$
✓
Answer
Correct option: B.
$\frac{ e }{4}-1$
(B) $\int_0^1 \frac{ e ^x(x-1)}{(x+1)^3} d x=\int_0^1 \frac{ e ^x(x+1-2)}{(x+1)^3} d x$ $\begin{array}{l}=\int_0^1 e ^x\left[\frac{1}{(1+x)^2}+\frac{-2}{(1+x)^3}\right] d x \\ =\left[\frac{ e ^x}{(1+x)^2}\right]_0^1=\frac{ e }{4}-1\end{array}$
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